Answer
$k=-\frac{16}{3}$
When $x=-3$, the value of $y$ is $16$.
Work Step by Step
Recall:
The formula for direct variation is $y=kx$ where $k$ is the constant of variation.
When $x=7$, the value of $y$ is $-16$.
Substitute these values into the equation above to find the value of $k$:
\begin{align*}
y&=kx\\\\
-16&=k(7)\\\\
\frac{-16}{7}&=\frac{k(7)}{7}\\\\
-\frac{16}{7}&=k\\\\
\end{align*}
Thus, the equation for the given direct variation is $y=-\dfrac{16}{7}x$.
To find the value of $y$ when $x=-3$, substitute $-3$ into the equation to obtain:
\begin{align*}
y&=-\frac{16}{3}x\\\\
y&=-\frac{16}{3} \cdot (-3)\\\\
y&=16
\end{align*}
